webpack.config.js
module.exports = { context: __dirname + \"/app\", entry: { javascript: \"./app.js\", html: \"./index.html\", }, resolve: {
You need to add presets to your babel-loader:
{ test: /\.jsx?$/, exclude: /node_modules/, loader: "babel-loader", presets: ['es2015', 'react'] },
http://babeljs.io/docs/plugins/#presets